Resolution is Cut-Free

Olivier Hermant (1, 2)

1 Departamento Sistemas Informáticos y Computación [Madrid]
2 ISEP - Institut Supérieur d'Electronique de Paris

In this article, we show that the extension of the resolution proof system to deduction modulo is equivalent to the cut-free fragment of the sequent calculus modulo. The result is obtained through a syntactic translation, without using any cut-elimination procedure. Additionally, we show Skolem theorem and inversion/focusing results. Thanks to the expressiveness of deduction modulo, all these results also apply to the cases of higher-order resolution, Peano's arithmetic and Gentzen's LK.

Mots clés: classical sequent calculus; cut-free; cut rule; deduction modulo; ENAR; resolution; rewriting; skolemization; Skolem theorem

Domaines: Automatique

Olivier Hermant. Resolution is Cut-Free. Journal of Automated Reasoning, 2010, 44 (3), pp.245-276. ⟨10.1007/s10817-009-9153-6⟩. ⟨hal-00743218⟩